Figure REF  shows this modulational instability of the resonant wavetrain for \(u_{+}=0.65\) . The instability of
the resonant wavetrain is now clear, in contrast to the example shown in Figure REF (b), with the breakup of the resonant
wavetrain as it propagates in \(z\)  now prominent. Each wave of the DSW generates a resonant wave as a DSW is a modulated
wavetrain [1]}. Figure REF  shows that these resonant waves within the DSW are also unstable. Figure
REF  further details the evolution of the instability of the resonant wavetrain and shows a transition from a
uniform wavetrain to a series of wavepackets. This detailed modulational instability evolution closely resembles
experimental photographs of Benjamin-Feir instability for water waves [2]}.
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